bifurcation plot in Matlab

hello

i am trying to plot system to find bifuraction value of bifurection parameter

my system is as shown

bifurcation parameter is tau which is a time delay between x and v .

when tau =0 the sysytem is stable

i prove mathemtically that for some tau >0 we will have hopf bifurcation in system

but when i use matlab (which is i am new in ) gives me unstable system then is stable

we should have stable and then unstable with oscilation and hopf birfucation

what i did wrong my be my codes is not good

can you please help me in that

clc;
clear;
close all;

Paramppp;

% This is the value of tau
% You can have same or different for x and v
% In this below example tau for x is 1 and for v is 0.5
%
%
% time max
tf=500;
%
t=linspace(0,tf,1000);
%
% This is the tau values staring at 1 then increasing by 0.5 and end at 5.
% You can change the numbers if you want

tau_start=7.5;
tau_finish=12;
tau_step=0.5;
%
for tau=tau_start:tau_step:tau_finish
%
lags=[tau tau];
%
%plot_r=((tau_finish-tau_start)/tau_step)+1;
%plot_rc=round(plot_r/2);
%
splot_count=((tau-tau_start)/tau_step)+1;
%
plot_r=ceil(sqrt((tau_finish-tau_start)/tau_step+1));
plot_c=ceil((((tau_finish-tau_start)/tau_step+1)/plot_r));
%
disp("tau");
disp(tau)
%
sol=dde23(@ddefunc,lags,@yhist,t);
%
t=sol.x;
y=sol.y;
%
subplot(plot_r,plot_c,splot_count)
%
%plot(t,y(1,:))
xlabel("t")
ylabel("x")
%
%plot(t,y(2,:),"r")
%xlabel("t")
%ylabel("y")
%
%plot(t,y(3,:),"g")
%xlabel("t")
%ylabel("virus partical")

%plot(t,y(1,:),"b",t,y(2,:),"r",t,y(3,:),"g")
title('tau') 
plot(t,y(1,:),"b",t,y(2,:),"r")

pause
end

[Abhinav Gangwar]

Hi, did you find the solution to your problem?

I am kind of stuck on a similar one.